QUESTION 2

Assuming the stock market model is modified so that the stocks going up tomorrow depends upon whether it increased today and yesterday. Precisely, if the stock has increased for the past two days, it will increase tomorrow with probability 0.85. If the stock increased today but decreased yesterday, then it will increase tomorrow with probability 0.65. If the stock decreased today but increased yesterday, then it will increase tomorrow with probability 0.5. Moreover, if the stock decreased for the past two days, then it will increase tomorrow with probability 0.3.

(i) Discuss the MC model for the modified stock market and state clearly any difficulty arising from the MC modelling process and the steps taken to resolve the challenge.

(ii) Draw a Transition Diagram to graphically represent the information in the Transition Matrix for the modified model and appropriately explain the meaning of the components of the graph.

(iii) Obtain an appropriate MATLAB code to compute the equilibrium probabilities for the modified MC model.